Plasma heating characterization of the large area inductively coupled plasma etchers with the plasma information for managing the mass production Open Access

Low-pressure RF (radio frequency) discharges applied in the semiconductor and OLED (organic light emitting diodes) display industries for thin film etching and deposition processes are changing our lifestyle drastically. With the adoption of memory and logic semiconductors, IoT (Internet of things) and AI (artificial intelligence) have become almost the default functions of electric devices. Various kinds of functions, such as flexibility, rollability, stretchability, speakability, and touching-sensibility, are included in the displays of smartphones, laptops, monitors, tablets, and even for car windows with high definition over 102 ppi (pixels per inch).^1,2 Their speed of development has been becoming more and more faster. This means that the pattern architecture, which should be fabricated by the plasma processes, has been changing fast to the more complicated and fine structures with the shortened period of the new model's launching.³ 

This hectic semiconductor and display industry trend is a severe mission to low-pressure RF plasma physics. For the given hardwares in the mass production facilities, which fabricate semiconductors and OLED displays, a drastic increase in the plasma process difficulties is a challenging issue caused by the new IT product model's launching. The process margin is generally constructed with the new patterning structures.⁴ Moreover, the mass production management strategy sensitively changes with the market situation. As a result, numerous plasma processing chambers should be controlled to perform the same process, even for the different kinds of reactors frequently. The detailed structures of each plasma source, e.g., antenna design of the inductively coupled discharge, are sometimes unknown for the process engineers because of the industrial security and international trade law.⁵ 

In many cases, this C2C (chamber-to-chamber) matching procedure of plasma etchers in the mass production factory is performed based on the process results and the EES (Equipment Engineering System) data, which include data from the various sensors attached to the processing reactors. However, it is very difficult for two reasons. The first reason is the nonlinear, complicated relation between process results and the sensed variables. The second one is the same plasma parameters, such as plasma temperature T_e and plasma density n_e, cannot guarantee the same process results. They are even difficult to measure in the mass-producing plasma chambers without perturbation to the system, with an acceptably small footprint. Therefore, the plasma processing engineers in the mass production factory perform the C2C matching using a trial-and-error case study. This process requires enormous effort and time but should be repeated for every new model's launch.⁶ Therefore, to reduce this massive loss in the semiconductor and OLED display industry, a reference index to match and tune the process chambers to achieve controlled process performance is needed rather than the raw sensed variables or T_e and n_e.

In this study, we introduced the new reference index applicable to C2C match in the OLED display manufacturing factory in terms of the PI (plasma information) parameters.^7,8 For the control of the mass production systems consisting of plasma processes, FDC (Fault Detection and Classification) and APC (Advanced Process Control) logic are required for maintaining high production yield. To achieve improved results of the process efficiently by application of the control logic, fast and in situ detection-based control of the process is required rather than batch-to-batch scale control. This implies that process results measured and inspected data should be provided as information in the performance variable form to develop practical process control algorithms. Most plasma-assisted processes are performed in a vacuum chamber, and a large number of unit processes are continuously proceeded; thus, direct measurement of the process results during the mass production is very difficult. This is why developing a VM (virtual metrology) model, which directs the process control, is needed. Cheng et al. explained that VM is a method for estimating the manufacturing quality of a process tool based on data sensed from the process tool and without physical metrology operations.^4,9 For the VM, various variables from the numerous sensors are adopted, and the quality of these variables governs the prediction accuracy and the cause analysis performance of the VM model. Increasing the number of sensed variables to include sufficient information from the sensor data in the VM modeling is advantageous for achieving better prediction accuracy of the VM algorithm; thus, many data scientists try to adopt super big data for machine learning (ML) and deep learning modelings with improvement of computational power. However, this strategy for developing VM or industrial process control logic faces the curse of dimensionality frequently. Statistically, at least 10 records per one variable (degree of freedom over 10) should be secured to obtain accuracy-guaranteed results.^8,9 Otherwise, the model is overfitted by the input data and loses its applicability to the new data and records. Because of the difficulty of obtaining a large number of measured or inspected records of the vacuum-based plasma process results during mass production, reducing the variables' number should be achieved simultaneously.⁷ This implies the importance of a “powerful input variable with enough information for modeling” rather than a large number of variables with insufficient information. Loh and Yun reported the selection of the sensor variables that are most likely to give “good information” is important to the performance of the VM algorithm.¹⁰ PI parameters, the indices synthesized from the sensed variables to represent the variation trend of essential physical meanings in the plasma processing reactions, could be one of the good strategies to reduce the dimension of the data matrix and obtain a higher degree of freedom for data handling. PI parameters were useful in enhancing the performance of the VM very efficiently.^8,11 They include information about plasma heating and sheath physics, plasma chemistry, and plasma-material surface reaction kinetics, which are essential for classical processing plasma analyzing models such as PIC (particle-in-cell) simulations, as domain knowledge, in general. The application of the PI parameters in VM modeling had the advantage of overcoming the curse of dimensionality because a smaller number of state variables were required compared to the general statistical VM models with good information.⁷ PI parameterization depends on the kinds of sensed variables of the observing system and the prediction target by the establishing VM model.

For example, to monitor the “power coupling efficiency” PI parameter in the observed OLED display manufacturing plasma etchers, we have applied the current–voltage signals and the reflected power from the each loop of the antenna coils recorded in the EES data pool of the mass production facility. The power coupling efficiency of each antenna loop with the plasma was calculated using the simple relation $η= ( P abs − I rms 2 R ) / P abs$⁠, where the absorbed power P_abs was determined using the subtraction of the reflected power P_ref from the input power P_in for each antenna coil. I_rms was adopted as the root mean square value of the monitored I–V sensor variables, and the impedance R of the coils was calculated in the same way introduced in Ref. 12. This power coupling efficiency representing the PI parameter has been applied to the previously reported PI-VM modelings to supply information about the power coupling characteristics of the plasma reactor, although this cannot exactly express the absolute quantity of the real power coupling efficiency. These PI parameter synthesizing methods based on the physical logic with applying sensed variables recorded in the EES data pool were effective in including the information about the physical parameters' varying trends. For the mass production facilities with limited various plasma diagnostics systems, which is almost impossible to measure the accurate plasma parameters, this PI parameterization strategy was powerful enough to overcome the weakness of the ML (machine learning) based statistical VM algorithms.¹¹ The smaller number of the inspected records for process results is required with reduced number of the state variables by adopting the PI parameters; thus, the shorter period is consumed to prepare dataset for VM modeling, and the computation for the VM can be efficiently lighter. This gives us the higher possibility for real-time prediction and monitoring of the plasma processes even during the mass production.

Most process resultants governing physical phenomena are strongly related to the electron heating mechanism in the OLED display manufacturing plasma etching reactors. Ohmic heating due to electron–neutral collisions and stochastic heating at the oscillating plasma edge due to momentum transfer from high-voltage moving sheaths occur simultaneously in the plasma etchers.^13–18 The ratio of Ohmic heating and stochastic heating determines the property of the electron heating; thus, electron-impact inelastic processes and the plasma–surface interactions are strongly correlated with the plasma processing results.¹⁵ Therefore, we suggested an electron heating mechanism representing the PI parameter as a new index to manage the huge mass production system and applied this index to match numerous plasma etchers. Finally, we could achieve the same process results from all of the reactors within a short period to prepare for the launching of the new OLED display models and could understand the characteristics of the large area inductively coupled plasma (ICP) sources applied to the OLED display manufacturing plasma processes.

In Sec. II, the characteristics of large-area inductively coupled plasma etchers with capacitive coupling were introduced, which is applied in the OLED display manufacturing factory. From the etching process performances in the different types of reactors, requirements on the new PI index to control and manage the mass production system were described. In Sec. III, electron heating mechanisms in the inductive discharges with capacitive coupling like observed OLED display manufacturing plasma etchers have been reviewed, and the possibility of PI parameterization for in situ monitoring was considered by using the optical sensor data. In accordance with the introduced new PI parameter, which represents the characteristics of the plasma heating, the processing recipe was optimized to achieve the required process results, and the C2C was performed based on the understanding of the process reaction mechanism in Sec. IV. Additionally, the performance of the new PI parameter for applying to the VM algorithm and mass production data was validated.

To meet the economic profit and mass productivity, 5.5 G (1300 × 1500 mm²), 6.0 G (1500 × 1850 mm²), and 8.6 G (2250 × 2600 mm²) large area target processing rectangular inductively coupled plasma (ICP) sources are adapted to the mass production of the OLED displays. Because the area of the glass, which is the etching target to manufacture the OLED display panel like the semiconductor wafer, is very large on a square-meter-scale, high process capacity is needed. Therefore, to obtain a high yield for the huge processing target with economical energy consumption, high plasma density achievable ICP type etchers have been applied in many OLED display manufacturing plasma processes.^12,19 To process large area rectangular glasses with 0.4 mm of thickness, a TCP (transformer coupled plasma) device-like placement of a planar antenna on the top side of the chamber was adopted. There are two types of inductively coupled plasma etchers adopted for the 8.6 G glass processing. The first type is 13.56 MHz frequency of RF power is transferred through this antenna; thus, current flows through this topside coil induce the plasma current near the top side of the plasma chamber within the skin layer of the plasma. The antenna and the plasma are separated by the Y₂O₃-coated dielectrics, and the processing gas is supplied through the gas holes distributed on the topside dielectric parts. On the bottom side of the chamber, ESC (electrostatic chuck) is placed to fix the glass during the plasma etching process. Right under the dielectric ESC, a plate-type bottom electrode is located to supply the bias RF power with a 3.2 MHz frequency. Six TMPs (turbo molecular pumps) are placed at the four corners of the reactor bottom and the center of the long sides on the bottom to pump the gas and byproducts. All of the plasma-facing walls are covered with the Y₂O₃ and Al₂O₃ ceramic-coated electric insulator, except the quartz viewport window to monitor the plasma by using the OES (optical emission spectroscopy) adopted as the EPD (end point detection) sensor. An optical fiber connected with the OES was attached to the viewport toward the center of the plasma, which is the exact center of the chamber's long side area. The second type of inductively coupled etcher is almost the same as the first type of etcher except for 3 points. 4.61 MHz of RF power is supplied through the antenna, and the thin metal layer similar to the Faraday shield is located between the antenna and the dielectric parts on the top side. The gap between the topside dielectric parts and the bottom electrode is about half of the first type reactor. The other properties of this second type of etcher are exactly the same as the first type. The location of the viewport, where the optical fiber adaptor has been installed, is at the exact center of the reactor's long side area. That is to say, the observed light using the OES from the second type etcher is closer to both the topside antenna and the processing glass than the first type etchers.

To achieve efficient power density in the large reactor, the reduction of the gap between the top and bottom sides is very important.²⁰ Only tens of centimeters are allowed space for the motion of meter-scale glasses carrying robots. Therefore, the reactors have larger area-to-volume ratios compared to the cubic structured ideal volume, and this changes the particle balance and power balance properties sensitively.

If we can reduce the A_eff by changing the chamber design, the slope of the straight line P_loss can be lower, like as P_loss' sketched as a red dashed line. In that case, the intersection of the P_loss' line with the I_rf < I_min curve also satisfies the inductive mode operation range. However, because of the power density limitation problem, the narrow gap large area reactor has difficulty avoiding steep slopes like the P_loss of the blue line. These characteristics of the large area reactor applied for OLED display manufacturing caused quite complicated phenomena during the etching processes. Therefore, gathering information about this equilibrium state of the plasma is important to understand the events that appeared in the etching processes in the large-area power density-limited reactors. Moreover, this can be a key PI index for the modeling of the VM to predict and control the plasma heating characteristics-related process deviations. This is why we have tried new PI parameterization in addition to the already existing PI parameters such as the “power coupling efficiency,” “electrode cooling efficiency,” “He instability,” “chucking force,” “exhaustion efficiency,” “ion energy,” and “plasma potential.”⁴ 

These power coupling properties also govern the characteristics of the plasma, and porcess results are also affected by them.^14,34–36 Therefore, capacitive coupling-driven standing wave effect and strong E_z have been considered to be suppressed in many cases. Faraday shield-like metal shielding parts between the current driving coil and the plasma are applied to decay E_z components to the plasma space for some devices.^20,22 Therefore, the second type etchers previously described have a majority to avoid standing wave effect-driven plasma process failures.

One of the most important plasma processes in the OLED display manufacturing system is the hybrid-metal layer target etching. To pattern the conducting wire of the micro-circuits, etching process of the metal target should be performed with the well-tailored etching profiles and with good uniformities for micro- and macro-scale. The dominant metal for patterning is aluminum, and the etching required area for patterning is very large as the size of the glasses; thus, the chemical etching reaction to form the Al_xCl_y compounds is the main process reaction mechanism by using the Cl₂ and BCl₃ gas based plasmas.^19,29 Dissociated Cl radicals, dissociatively ionized Cl⁺ ions, and excited Cl₂ molecules react with the Al target and form Al_xCl_y byproducts. These compounds are volatile for x:y = 1:3, and their volatility decreases with the x/y ratio.^19,37 Therefore, inelastic collisional process rates with electron impact are critical factors to control this etching process.

More than the etching reaction itself, tailoring the etched profile is also essential to achieve the proper performance of the OLED display panel. In particular, control of the taper angle at the sidewall of the etched pattern is one of the critical factors for driving circuits of the OLED display. To control the sidewall taper angle during the photo resist material mask applied etching process, passivating gases such as N₂, O₂, or H₂ have been proposed to be added into the Cl₂-based plasma chemistry, as Chanson et al. had reported.^38–42 The increase in the atomic nitrogen flux enhances the passivation of the sidewall surface; thus, the dissociation reaction of N₂ molecules in the plasma is very important to pattern the profile.^38–42 The observed process in this study is this aluminum-based titanium and molybdenum metal hybrid layer etching by the Cl₂ and BCl₃ gas-based plasmas with adjusting N₂ gas addition to tailor the etching profile. The partial pressure of the Cl₂:BCl₃ is kept at about 3:1 at the 10 mT pressure, and the source power supplied by the antenna is decided by the total thickness of the metal etching target and the required etching process time. The bias power supplied at the bottom electrode was about 20% of the source power in the observed process.

Figure 2 represents the optical emission spectra in the visible range observed during the plasma etching process of the aluminum-based metal hybrid target. Two types of etchers are observed for 13 reactors introduced in Sec. II A. The spec of the etching targets, including the thickness and structure of the metal layer, was the same for all of the 13 reactors; thus, the detailed processing recipe was also the same. Spectra of the first type of etchers (Type I) are sketched with gray graphs, and those of the second type of etchers (Type II) are sketched with blue graphs. The overall spectra of these two types of etchers have very big differences from each other, which is strongly correlated with the etching profile.

For type I etchers with 13.56 MHz RF power supplying, light emissions of N₂ first positive system (B³Π_g → A³Σ_u⁺) at the range of 550–800 nm are noticeable compared to the spectra of type II etchers. As shown in Fig. 3, the lowest threshold energy of the electron impact light emission of the N₂ molecule is the first positive system of 7.35 eV.^43,44 The spectra of type II etchers with metal shield parts and 4.61 MHz RF power supply do not show the noticeable emission of the N₂ first positive system. On the other hand, spectra of the type II etchers have various kinds of emissions. Dissociated or ionized processing gases such as B, Cl, N, and N₂⁺ lines and byproducts such as AlCl, BCl, and TiCl emissions are observed. Some sputtered-out metal atomic emission lines of Al, Al⁺, and Ti are also observed.⁴⁵ 

With an abundance of atomic nitrogen, type II etchers are advantageous for tailoring the etching profile to have a more gradually sloped sidewall due to the passivation effect on the sidewall. Table I shows the process results in the two types of etchers observed as the emission spectra of Fig. 1. As dissociated processing gases were observed more in type II etchers, the overall etch rate was higher, about 5% in type II etchers. Non-uniformity, which is defined as the etch depth difference between maximum and minimum values in one glass, was about half of type I etchers in type II etchers. Namely, more uniform process results were achievable in type II etchers. The taper angle of the etched pattern's sidewall was smaller, about 10.2° in type II etchers. This taper angle is defined as the angle between the bottom of the etched hole and the surface of the sidewall. It means that the side walls of the etched pattern in type I etchers were almost vertical, while the side walls patterned in type II etchers were relatively oblique. The purpose of sidewall passivation in this metal etching process for OLED display manufacturing is to form the lower sloped oblique sidewall, unlike the vertical HARC (high aspect ratio contact) patterning of the semiconductor production.¹² As nitrogen atomic peak has been observed in type II etchers, N atom-assisted sidewall passivation was more enhanced and taper angle was smaller in type II etchers.

However, these noticeable differences in process performance between the two types of etchers are severe drawbacks in mass production. Process results should be controlled by a specification required to mass-produce the OLED display or semiconducting devices. Different performances of the process reactors make the control of the mass production management difficult because the processing recipe or the detailed plasma-facing parts of the reactors should be customized for each reactor. In the practical fields, usually, the optimization procedures of the processes for each of the reactors are performed by trial and error of the process results. This takes a long time and effort of the engineers; thus, quite a significant loss of productivity in the mass production fab. Even this optimization required period has become shorter and shorter according to the more and more frequent new model launching of the IT devices. Therefore, if we can introduce the reference index to characterize the process chamber's performance properties even monitorable in the mass production system with limited diagnostics, this would efficiently decrease the loss of mass production management.

In this study, we suggest this reference index for the inductively coupled plasma etchers with capacitive coupling in terms of the plasma heating mechanism. We selected this as a key PI parameter to characterize the reactor's performance, as stated in Sec. III.

As previously described with schematics of equilibrium in the inductively coupled plasma system of Fig. 1, it is difficult to operate the very large ICP devices that we have been observing within the perfectly inductive mode without the capacitive coupling.⁴⁶ We cannot exclude the consideration of the capacitive RF discharges' properties in the OLED display manufacturing plasma etchers what we have observed.

Godyak introduced the electron power deposition for a dc sheath with a small sinusoidally vibrating fluctuation and put forward the idea that Fermi acceleration might be a major mechanism to sustain capacitive discharge at low gas pressures.⁴⁷ These ideas were further developed by Godyak et al.⁴⁸ An explicit application of Fermi acceleration to electron heating in RF discharges was by Godyak:⁴⁷ 

Gabor et al. stated the sheath width oscillates, and electrons reflecting from the sheath are velocity dispersed. They stated the electron interaction with RF oscillations in the sheath generates a high energy tail of the EEDF (Electron Energy Distribution Function).^47,49 Gould explained that the electron reflection in the oscillating sheath is accompanied by RF energy absorption, due to a type of transit time heating.^47,50

Although both heating mechanisms contribute to the increase in plasma density and overall energy of the system, the roles of each heating to the plasma etching reactions are very different. Gudmundsson et al. analyzed with the Monte Carlo simulation that the effects of Ohmic heating and stochastic heating on the IAD (ion angle distribution), IED (ion energy distribution), and EED are very different from each other.^57,58 This means that the information about the heating mechanism in the etching plasma can give us an understanding of the characteristics of the etching properties, i.e., the contribution of the ion-assisted physical etching and neutral species-based chemical etching. Therefore, we have tried to parameterize the PI index, which represents the heating mechanism of the plasmas.

One of the most general analysis methodologies to understand the power coupling mechanism in one inductively coupled plasma reactor is observing the E–H transition by scanning the RF power.^59–63 To obtain information about the power coupling mode of the observed system, we have changed the RF power supplied through the antenna coil of two types of the etchers. For type I etchers, the RF power has changed from 3 to 34 kW for 10, 20, 30, and 100 mT of the pressure, and for type II etchers, RF powers of 2–14 kW for 10 mT, 2–9 kW for 20 mT, 2–10 kW for 30 mT have supplied. Both etchers discharged pure Ar gas, and bias power was not supplied to the bottom electrode; thus, the only power applied to the Ar plasma is 13.56 and 4.61 MHz source powers flow through the coils for type I and type II etchers, respectively.

The spectra monitored by using the OES sensor have been analyzed into the plasma parameters with the application of the diagnostic methodology introduced to develop the various PI-VM (plasma information based virtual metrology) models in the OLED display manufacturing fab.^4,7,34 This model adopted CE (corona equilibrium) state, which is a simple approach to population densities in non-equilibrium plasmas having relatively low electron density (≈10¹² m⁻³) and negligible probability of electron impact de-excitation processes like as the solar corona.^64,65 Therefore, the corona model assumes that upward transitions are only due to electron impact collisions, while downward transitions occur only by spontaneous radiative decay.⁶⁵ 

Both T_e,eff and n_e of the two types of etchers show different tendencies with varying RF power and pressure. T_e,eff of the type II etcher is higher than that of the type I etcher in the overall range of the power and pressure and more drastically decreases with the RF power and is more sensitive to the operating pressure. Plasma density n_e increases with RF power for both types of etchers, but the n_e of type II etcher is lower noticeably when pressure is 10 mT. For type I etchers, the electron density n_e seems to be saturated over about 15, 14, 12, and 10 kW for 10, 20, 30, and 100 mT, respectively; thus, this power range is expected as the E–H transition region for type I etchers. However, this transition was not clearly observable in type II etchers because of the applicable power limitation. These T_e,eff and n_e are very typical and important information about the plasmas, but it is difficult to understand the properties of the etching process and the characteristics of the process reactors directly. As previously stated, we have tried to parameterize the new PI index, representing the plasma heating characteristics.

Using the T_e,eff and n_e in Fig. 5, we have calculated $S stoc ¯$ and $S ohm$ of Eqs. (13) and (17). Calculated Debye length λ_D and wall potential in the argon discharge $Φ w | Ar$ are shown in Fig. 6. The time-averaged sheath potential $V ¯$ is one of the important parameters to calculate Eq. (13) and is generally determined using the lumped element circuit models.^{22,46,67–69} However, in many cases, these models are not appropriate to calculate the sheath potential of the plasma processing devices in the mass production fab because of the too complicated and unknown detailed structure and design of power coupling parts to the plasma, as previously stated.

The effective collision frequency ν_eff of Eq. (20) is needed to calculate absorbed power density. Lieberman and Godyak analyzed this effective collision frequency with varying pressure and explained the difference between ν_eff and ν_m is the effect of stochastic heating. The variation of ν_m is explained due to Ohmic dissipation alone.^22,47,48 The results in Fig. 7 can also be analyzed in a similar manner. Figures 7(a) and 7(b) represent the variation of the ν_eff and ν_m with increasing n_gT_e,eff rather than pressure for type I and type II etchers, respectively. The type I etchers with larger L show a very small difference between ν_eff and ν_m, while the type II etchers with smaller L and metal shielding parts show about 2  $×$ 10⁷ s⁻¹ of difference between ν_eff and ν_m. This result shows that the plasma heating mechanism of the type I etcher is dominated by Ohmic heating, while the type II etchers also transfer the power to the plasma with stochastic heating, also. Classical definition of this effective collision frequency introduced by Godyak et al. with the moving rigid wall concept to the collisionless electron heating operates very effectively to explain the observing large area ICP with capacitive coupling.⁴⁸ 

Finally, the calculated result of the S_stoc/S_ohm according to Eqs. (13) and (17) is shown in Figs. 8(a) and 8(b).

As expected from the analysis of ν_eff, the contribution of stochastic heating is much larger about one order for type II etchers compared to that of the type I etchers. S_stoc/S_ohm rapidly decreases with increasing RF power, that is to say, decreases with increasing n_e and larger with lower pressure conditions for both types of etchers. This trend represents well the characteristics of the collisionless power absorption property of the stochastic heating mechanism. From this result, we can understand that the power coupling characteristics of the two types of etchers are very different; plasmas in the type II etchers are more capacitive discharges compared to those of the type I etchers. Although both types of etchers are designed as large-area ICP reactors, they have non-negligible capacitive coupling properties, and this characteristic is much larger for type II etchers. Of course, detailed assumptions driving Eqs. (13), (14), and (17) give different values as Kawamura et al. described according to the mobile-ion, fixed-ion, fluid model, and hard wall limit conditions.^72,73 Adoption of the wall potential to the time-averaged sheath potential for calculating S_stoc/S_ohm might cause underestimation of this PI parameter for relatively higher power (about >10 kW) applied regime by the low-voltage limitation as Godyak and Riemann suggested.^70,71 However, overall trend analysis with varying power and pressure for different types of reactors was possible because the under-estimated amount of wall potential shift is $T e[ ln I 0 ( V T e )]$⁠, which is determined by the gradually increasing simple modified Bessel function in the range of observed system.²⁰ By introducing the PI index representing the stochastic heating power density to Ohmic heating power density ratio, we could easily understand the plasma heating characteristics of the observed etchers as the plasma sources. From this result, we could analyze the very different process results in the two types of etchers and applied to manage the mass production system as stated in Sec. IV.

Here, n_g,j is the gas number density of species j, σ_j, and E_th,j are the excitation cross section and threshold energy of the species j, respectively. This is determined by the number of electrons with energies over the reaction threshold energy and the number density of reactant gas, n_g,j.

Figures 9(a)–9(c) represent the densities of electrons that have energies higher than 1.18, 7.35, and 10 eV, respectively, estimated regarding the results in Fig. 5. 1.18, 7.35, and 10 eV denote the threshold energies of the reactions strongly correlated with the observed metal etching process. As shown in Fig. 3, the light emission of N₂ first positive system is contributed by the electrons with the energy over 7.35 eV for ground state N₂ molecule and 1.18 eV for N₂ (A³Σ_u⁺). For the etching processes pressure, 10 mT, the numbers of the electrons with ε > 1.18 eV and ε > 7.35 eV in the type II etcher are noticeably lower than that in the type I etcher. Because of this, emission of the N₂ first positive system was not observed in type II etchers during the etching process, even though the process recipes of both types of etchers were the same, as shown in Fig. 2. On the other hand, the number of electrons with ε > 10 eV was much larger in the type II etcher compared to the type I etcher for all of the observed pressures. As shown in Fig. 3, the dissociation of the N₂ molecule in the ground state has 9.8 eV of threshold energy.^43,44

Moreover, electronic excitation cross sections of the molecular N₂ are especially high at the energy range of 10–12 eV, as Song et al. reported.⁷⁴ They stated that N₂ is a common gas, but its cross sections are uncommon with the resonant character of some of the electronic excitation channels (and high values of these cross sections, both for triplet and singlet states), high cross section for the dissociation into neutrals, and high cross sections for elastic scattering (and electronic transitions) on metastable states. This causes especially high sensitivity of inelastic processes, including the light emission and dissociation in the N₂-aided plasmas to the electron densities with energy over about 10 eV.

Figure 9(c) shows more than 10 times higher number density of the ε > 10 eV electrons for type II etchers than for the type I etchers; thus, dissociation, ionization, and dissociative ionization like electron impact inelastic processes of N₂ molecules are more reactively occurred in the type II etchers rather than the low energy electron assisted vibrational excitation or first positive system excitation. This thermodynamic equilibrium state characteristics of plasma lead to sufficient sidewall passivation and etching profile taper control available condition for the metal etching processes with the N₂ added plasmas.

The analysis of the characteristics of the two-type etchers implies that the capacitive power coupling property is stronger in type II etchers rather than in type I etchers. These characteristics of the reactors resulted in the different process performances in two types of etchers, as shown in Table I. Enhancement of the collisionless stochastic heating in the plasmas caused a slightly higher etch rate with the assistance of the higher energy ions and reactive radical flux, better spatial uniformity of the process results, and sufficiently passivated sidewalls with a lower taper angle. To achieve similar process results in the type I etchers with the type II etchers for mass production, we have tried compensation of low S_stoc/S_ohm of type I etchers by tuning the process condition.

As Gudmundsson and Rauf had directly shown, electrostatic power deposition of the plasmas is clearly concentrated at the sheath region.^57,58,75 That is to say, to compensate for the etching process performance of the type I etchers with type II etchers, the tune of the sheath property-related parameters should be more effective than any other parameters. We could approach this compensation with two factors. The first one is the energy matching of the ions accelerated through the sheath, and the second one is tuning the dissociated neutral nitrogen flux onto the substrate generated by the stochastically heated high-energy electrons from the sheath. These two factors are strongly related to the etching process results and are governed by the sheath of the plasmas.

The first factor is tuned by the changing bias power on the bottom electrode, in which the etching target glass lies. Figure 6(b) shows the difference in the wall potential in the two types of etchers without the bias power. This denotes that the ion energy arrived at the reactor wall through the sheath is nearly 2.5 times larger for type II etchers in 10 mT than for type I etchers in the default condition. According to this, we have tried to adjust the ion bombarding energies arrived at the etching target surface by increasing the amplitude of the bias RF power. Because the ion frequency of the observed plasma reactors was distributed from 4.9 to 66 MHz for Ar⁺ and Cl₂⁺, the ion transit time across the sheath formed by the 3.2 MHz bias power is slightly shorter than the bias RF period. Consequently, the energy that ions gain by the acceleration in the sheath can be increased with the amplitude of bias power; thus, we have increased bias power 2.5 times larger than the original recipe in the type I etchers first, with a very rough approach. Of course, bias power itself is not directly proportional to the ion energy bombarded onto the bottom electrode, but the low frequency of 3.2 MHz bias power can contribute to the acceleration of the ions in the given system efficiently. The increase in bias power with the fixed source power was nearly independent of the electron density in the observed system; thus, we could roughly approximate the ion energy would be enlarged with increasing bias power.

Table II shows the etching process results and atomic N and Cl monitored results of the bias power and N₂ partial pressure modified cases in type I etchers. Every condition was tested for 28 sample glasses (1 lot), and the averaged process results were arranged. Measured etch rate, uniformity, and taper angle had about 5%, 9%, and 2% standard deviations, referring to the averaged values for one lot of glasses. Type I|_ref and Type II denote the original condition introduced in Table I with the original processing recipe. Type I|_N2 × 5, Type I|_N2 × 10, and Type II|_N2 × 20 represent 5 times, 10 times, and 20 times of N₂ partial pressured increased cases with 2.5 times larger bias power supplying, respectively. With the original processing recipe the same as that of type II etchers, the etch rate was lower, process uniformity was worse, and the taper angle was higher to achieve the proper mass production performance of the OLED display. With increasing N₂ partial pressure, N atomic flux-driven passivation is enhanced; thus, the taper angle of the etched pattern sidewall has decreased. As we had introduced previously, achieving at least 20° lower sidewall taper angle with a gradual slope than the vertical sidewall is important for the quality of the OLED display performance.⁴ Therefore, considering the taper angle of the process results, 10 times or 20 times of N₂ partial pressure set process condition was selectable to get a similar taper angle with type II etchers in type I etchers. However, because of the too-low partial pressure of Cl₂ with 20 times of the N₂ gas input, the metal etching process rate by the reaction with Cl radical, Cl₂⁺, Cl⁺ ions, and excited Cl₂ molecules is too lowered for the Type I|_N2 × 20 case. Moreover, non-uniformity was 42% higher than in the type II etchers to select Type I|_N2 × 20 by the drastically increased n_e and shortened λ driven standing wave effect.^23,24 On the other hand, for low N₂ partial pressure adopted cases, Type I|_ref and Type I|_N2 × 5, high electronegativity driven stronger capacitive power coupling caused vertical electric field related standing wave effect and non-uniform distribution of the plasma as Rauf reported.⁷⁵ As a result, we could choose Type I|_N2 × 10 condition for type I etchers to achieve controlled etching process results similar to type II etchers.

[N]_norm in Table II represents the normalized intensity of N I 747 nm measured by the OES for each process condition. To compare the relative amount of the atomic N, the intensity of 746 nm was divided by the integrated area of full spectra. Full spectra in visible rays reflect the light emission of various gases consisting of that plasma; therefore, normalization by the area of the full spectra represents the partial pressure of atomic N. With increasing N₂ partial pressure of type I etcher, [N]_norm increases up to a similar level of type II etcher. This explains the decrease in the taper angle to be a more gradual slope with the addition of N₂ reasonably. [Cl]_norm represents the normalized intensity of Cl I 754 nm by the full spectra area. 754 nm line is one of the persistent lines of the Cl atom in the 200–800 nm visible range. [Cl]_norm of the Type I|_ref is 80% larger than that of Type II, and this can explain the similar etch rates of two types of the etchers without the process tuning, although the etching profile is very different. The abundance of Cl radical in the chamber could overcome the weakness of the ion bombarding energy onto the etching target. With addition of N₂, [Cl]_norm is drastically decreases, and even drop under the half of type II etcher for Type I|_N2 × 20 case. This explains the sudden drop of etch rate in Type I|_N2 × 20 by the lack of Cl radical and Cl₂⁺, Cl⁺ ions.

As expected from the analysis of the new PI index, S_stoc/S_ohm, the enhancement of the ion energy and N neutral-driven passivation by increasing the bias power and N₂ partial pressure was effective in controlling the process result in terms of the chamber-to-chamber matching.

Figure 11 represents the calculated electronegativity of the N₂-added Cl₂-based plasma with regard to Eq. (31) for varying molar fraction of N₂, n_N2/n_g, for T_e = 1, 2, 3, 4, 5, 6, and 7 eV. n_g is fixed to constant for pressure 10 mT, which is the observed processing condition. With increasing n_N2/n_g or T_e, electronegativity decreases rapidly for both cases. If the partial pressure of N₂ increases about 10 times, α decays under 1/2.5 of the initial value for all calculated electron temperatures. As previously stated, n_e⟨σv⟩ of Type I|_ref to generate the neutral N atom is about 30 times smaller than that of Type II etchers, but the best-compensated condition is Type I|_N2 × 10. We have expected that changed ne by the variation of α leads smaller adding of N₂ than 30 times could compensate the atomic N generation rate, and the result of Fig. 11 verifies this. Also, 10 times increase in n_N2/n_g and about 2.5 times increase in n_e by decayed α could match the atomic N generation rate in type I etchers with the level of type II etchers.

To verify the general applicability of the introduced PI index, S_stoc/S_ohm, for the modeling of PI-VM as reference information, we have tested the performance of S_stoc/S_ohm for the previously introduced PI-VM model.¹² The reported PI-VM model in 2021 was modeled to predict micro-range etching profile non-uniformity-driven OLED display performance faults. According to the PI parameters analysis, we could understand that the process fault was caused by the too-strong ion bombarding energy-related surface temperature and polymer precursor sticking probability changes. Introduced PI parameters parameterized from the EES and OES dataset were chucking forceof the ESC (Electrostatic Chuck), “center to edge ratio of the antenna power coupling,” “decay time constant” of the glass backside cooling helium gas flow after injected through the helium hole on the ESC surface, “He flow instability” caused by unstable chucking of the glass with the broken balance between chucking force and helium flow driven upward force, “non-uniformity of the electrode cooling” from the chiller coolant flows, “micro-geometry of the electrodes” which governs the heat transfer property in the materials contacted points, and “sputtered out Y-atom” monitored from the line emission intensity of yttrium atom. More than any other parameters, the contribution of the sputtered out Y-atom parameter for deciding the process fault to the introduced PI-VM model was noticeable. Because a large area of the plasma-facing parts in the observed chamber was Y₂O₃ to avoid the aging and erosion of the parts from the various chemical species, light emission from the sputtered-out Y atom represented the overall ion bombarding energy and flux. Y₂O₃ is a chemically very stable material in the etching process plasmas; thus, it is damaged only by the physical sputtering of the ions.

Figures 12(a) and 12(b) recall the representative PI parameters introduced in 2021 for 13 chambers during the sample period with the classified level of process faults.¹² The sample period was one week, and a fixed etching process recipe and etching target model were introduced for all 13 chambers with the same spec during the observation. During the observed sample period, 4433, 2525, 1284, 1336, 589, 503, 527, 1523, 1366, 280, 965, 1211, and 98 glasses were analyzed for the chamber 1, 2, …, and 13, respectively, and PI parameters were monitored for all glasses and averaged for each of the chambers. The etching process fault cases by the micro-scale non-uniformity of the etching profile were classified into levels 0, 1, 2, and 3 according to the inspected fault occurred frequency. Fault-free chambers were classified into level 0, and fault-occurred chambers with low- and high-frequency, but the mass production yield is spec-in cases, were classified into levels 1 and 2, respectively. Chambers in which fault occurred too frequently to maintain mass production were classified as level 3. According to the level of chambers, the management strategy of the process is determined in the mass production fab. For level 0 chambers, the process is performed continuously, and for level 1 and 2 chambers, the process is kept restrictive with the limited processing targets and with more frequent ISD (In Situ Dry cleaning) compared to the normal case. For level 3 chambers, the mass production is stopped, and the PM (Preventive Maintenance) procedure is performed.¹² 

As previously introduced in 2021, sputtered out Y-atom and “center to edge ratio of the antenna power coupling” had a strong correlation with the level of process fault compared to the other PI parameters, with 75.2% and 37.0% of Pearson correlation coefficients (R²), respectively. They are parameters including reasonable information related to the spatial gradient of the ion flux-driven surface passivation non-uniformity and another expression caused by the same phenomena with the observed process faults.

Figure 12(c) shows the newly parameterized PI index, “S_stoc/S_ohm,” in Sec. III B with the level of process faults for 13 chambers of 16 640 processes glasses. The S_stoc/S_ohm PI parameter also shows a good correlation with the level of process faults, and a reasonable explanation about the correlation with the other 2 PI parameters is possible. Correlations(R) between sputtered out Y-atom and S_stoc/S_ohm and center to edge ratio of antenna power coupling and S_stoc/S_ohm are 0.894 and −0.747, respectively. With high capacitively coupled power, a stronger spatial electric field caused higher ion bombarding energy transferred on the etching target; thus, line emission of sputtered-out material and S_stoc/S_ohm have a high positive correlation. The bad balance between center and edge power coupling property, that is to say, a large difference of power coupling efficiency between the central antenna loop and outer antenna loop calculated for each coils with the η_antenna introduced in the Introduction, means the large imbalance between current flows of the antenna.^12,83,84 This strong imbalance of the current causes the spatial non-uniformity of the electromagnetic field and the plasma distribution. As Perret and Rauf analyzed, this non-uniform spatial distribution of the strong vertical electric field is strongly correlated with the standing wave effect or skin effect, which are governed by the capacitive properties of the plasmas even in the inductively coupled discharges.^23,24,26,36 Therefore, a high correlation coefficient R with a negative direction between S_stoc/S_ohm and center to edge ratio of the antenna power coupling could be understood.

Figure 13 compares the correlation coefficients, R², between the level of process faults and previously introduced PI parameters in Ref. 12, and also between the level of process faults and the newly introduced S_stoc/S_ohm index. Information about the plasma heating properties-including-index, which could explain the phenomena in the processing reactor effectively, shows the best correlation with the process, which results in a very important characteristic to apply for VM modeling as a PI parameter.^11,14 As Edamura et al. discussed, the fraction of the capacitively coupled plasma (CCP) to the total plasma generation is one of the most important properties that govern the performance of the etching process reactors and the process results in the chambers.¹⁴ Characterization of the power coupling properties of the observing plasma reactor was helpful in understanding the process results difference between chambers and their performance matching by the optimization of the etching process recipes, and it was demonstrated that the applicability of this index to the PI-VM modeling for analyzing and managing the events in the mass production line which includes good information about the condition of the processing plasmas.

For mass production of the OLED display panels, a very large area plasma reactor, which is suitable for meter-scale targets with high production yield and throughput, is required. Because of this, inductively coupled plasma sources with higher plasma density compared to the CCP (capacitively coupled plasma) etchers have been adopted in many cases. However, because of the too large plasma-facing surface area-driven power loss compared to the applied power, the overall power coupling efficiency of the reactors is not ideal. This caused various kinds of reactor designs to enhance the plasma heating efficiency, and deviations in the process results were also driven. To perform the mass production, process results should be equalized without the process fault; thus, chamber-to-chamber matching based on the plasma properties was necessary. The introduced index this time, with characterization of the plasma heating mechanism, S_stoc/S_ohm, was efficient to analyze the power coupling properties of each reactor. With the information given by the S_stoc/S_ohm PI index, optimization of the mass production etching process recipe and understanding of the capacitive coupling in the inductive discharge was possible. Verification of the performance as a PI index was demonstrated for 13 chambers and 16 640 glasses, and we have validated the applicability of the S_stoc/S_ohm index to the PI-VM modeling to analyze the various issues in the fab during the mass production and to manage and control the plasma processes to achieve the optimized efficiency. This characterization of the plasma heating properties in terms of the PI index has shown the applicability of basic plasma physics, even for the lack of the detailed diagnosed plasma parameters and sensors, to the control and governing area of industrial plasma processes applied in the mass-producing systems. The introduced PI index based on the plasma heating mechanism is expected to be applied to the practical reference index to model the data-driven plasma control logic and collaboration with the AI (artificial intelligence) for plasma processes such as the PI-VM modelings.

This work was technically supported by the executive vice presidents Jaehyung Lee, Jeonggen Yoo, and Kyung-Han Kim of the mobile display business in Samsung Display Co., Ltd. The authors would like to thank their support sincerely. This research was supported by the Brain Korea 21 FOUR Program (No.4199990314119) and the National Research Council of Science & Technology (NST) grant by the Korea Government (MSIT) (No. CRC20014-000).

The authors have no conflicts to disclose.

Seolhye Park: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Methodology (lead); Project administration (lead); Software (lead); Writing – original draft (lead); Writing – review & editing (lead). Yoona Park: Data curation (supporting); Software (supporting). Jaegu Seong: Conceptualization (supporting); Formal analysis (supporting). Haneul Lee: Conceptualization (supporting); Resources (supporting). Namjae Bae: Conceptualization (supporting); Resources (supporting). Ki-baek Roh: Conceptualization (supporting); Software (supporting). Rabul Seo: Resources (supporting). Bongsub Song: Data curation (supporting). Gon-Ho Kim: Conceptualization (lead); Supervision (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.